Connecting elasticity and effective interactions of neutral microgels: the validity of the Hertzian model

TL;DR

This study investigates the link between single-particle elasticity and bulk behavior in microgels, validating the Hertzian interaction model through theoretical calculations and experimental comparisons.

Contribution

It develops a methodology to compute elastic moduli and effective interactions of microgels, demonstrating the Hertzian model's validity up to moderate packing fractions.

Findings

Reproduces experimental features like Poisson's ratio minimum near VPT

Hertzian model accurately describes interactions at moderate densities

Provides a general approach applicable to various soft particles

Abstract

An important open problem in materials science is whether a direct connection exists between single-particle elastic properties and the macroscopic bulk behavior. Here we address this question by focusing on the archetype of soft colloids: thermoresponsive microgels. These colloidal-sized polymer networks are often assumed to interact through a simple Hertzian potential, a classic model in linear elasticity theory. By developing an appropriate methodology, that can be generalized to any kind of soft particle, we are able to calculate all the elastic moduli of non-ionic microgels across their volume phase transition (VPT). Remarkably, we reproduce many features seen in experiments, including the appearance of a minimum of the Poisson's ratio close to the VPT. By calculating the particle-particle effective interactions and the resulting collective behavior, we find that the Hertzian model works well up to moderate values of the packing fraction.